This is a serious query. Due to its subject matter, nobody takes it seriously, but the answer is important to young and old people alike, all around the globe.
Can you burst a gut trying to “beef up” a fart (either to make it louder or to feel greater relief?)
I have read that if you “push” in order to better evacuate your stools, you might end up with hemorroids, a fate sufficiently grim. But, can you burst a gut by doing that?
No. Simply no.
Because the pressure from such a maneuver is external to the gut lumen, it does not result in bursting the gut nor does it strain the intestinal wall.
Various hernias, from the diaphragm to the umbilicus to the inguinal region, can result or be exacerbated. Venous backpressure, particularly with chronic straining, can cause or aggravate hemorrhoids.
A reflex vagal reaction, coupled with (temporarily) diminished venous return may drop your blood pressure and cause you to faint before the audience gets a chance to do so, diminishing your pleasure.
For a particularly remarkable production, it may be worth it, I suppose.
Probably not in the way the OP is saying. But I seem to recall one Mythbuster episode where they proved that if you downed a large quantity of Sodium Bicarbonate and 5 cokes, combined with your stomach acid it would be enough to rupture your stomach (which is aprox. equal to ‘burst a gut’ I suppose).
-XT
Farting, straining at stools, holding in or applying extra evacuation pressure, none of these will cause a prolapsed rectum.
A prolapsed rectum, like hemorrhoids, is a condition that results from long term weakening of the muscles. It does not come from a single event. It certainly doesn’t result from farting.
Seems to me most corpses have busted guts from the decay process. That’s why mummies had their innards removed.
IIRC they had the stomach openings firmly clamped off. In an actual person I think a burp would squeeze out long before it burst.
First, let’s define terms. “Burst a gut” could mean either blowing out a part of the alimentary tract, somewhere between the throat and the anus, or blowing out part of the abdominal wall, that sheet of muscle and connective tissue that keeps your innards from falling out.
Bursting any part of the alimentary tract is very unusual, except from violent injury. Bursting through the abdominal wall is more common, and we call it hernia. Most often, we get them from improper lifting, but not always. The surgeon who patched both of mine told me they happen from many things, including hard sneezing and coughing. Could you get a hernia from beefing up a fart, or even a Captain Beef Fart? 
I don’t know.
I asked the surgeon after my first hernia how I could avoid getting one on the other side. He said, “Choose other parents.” It’s genetic.